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Proof step 1245 from proof refine-truncate-buff-none-uncached (previous step)

(∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) ↔ n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m ∈ cache_icache, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m, cache_pcache0)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 1246:
cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m ∈ cache_files, n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) ↔ n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), m ∈ cache_icache, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m, cache_pcache0), m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Rule argument

fma: n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)%⊦ key ∈ truncate(ino, size, pcache) ↔ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino); (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (s) Used formulas: n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))